Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids

In an important series of articles published during the 1970s, Krasiński [Acta Phys. Pol. B 5, 411 (1974); 6, 223 (1975); J. Math. Phys. 16, 125 (1975); Rep. Math. Phys. 14, 225 (1978)] displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotatin...

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Bibliographic Details
Published in:Journal of mathematical physics 2023-02, Vol.64 (2)
Main Author: Célérier, M.-N.
Format: Article
Language:English
Subjects:
Einstein equations
Equations of state
General Relativity and Quantum Cosmology
Mathematical analysis
Physics
Rotating cylinders
Rotating fluids
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Summary:In an important series of articles published during the 1970s, Krasiński [Acta Phys. Pol. B 5, 411 (1974); 6, 223 (1975); J. Math. Phys. 16, 125 (1975); Rep. Math. Phys. 14, 225 (1978)] displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of a perfect fluid. However, these solutions depend on an unspecified arbitrary function, which leads the author to claim that the equation of state of the fluid could not be obtained directly from the field equations but had to be added by hand. In the present article, we use a double ansatz, which we have developed in 2021 and implemented at length into a series of recent papers displaying exact interior solutions for a stationary rotating cylindrically symmetric fluid with anisotropic pressure. This ansatz allows us to obtain here a fully integrated class of solutions to the Einstein equations, written with the use of very simple analytical functions, and to show that the equation of state of the fluid follows naturally from these field equations.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0131945